Asymptotic analysis of synchrosqueezing transform—toward statistical inference with nonlinear-type time-frequency analysis
Matt Sourisseau, Hau-Tieng Wu, Zhou Zhou
The Annals of Statistics · 2022 · Volume 50 · Issue 5
Abstract
We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and nonnull cases. The intricate nonlinear interaction of different quantities in SST is quantified by carefully analyzing relevant multivariate complex Gaussian random variables. Specifically, we provide the quotient distribution of dependent and improper complex Gaussian random variables. Then a central limit theorem result for SST is established. As an example, we provide a block bootstrap scheme based on the established SST theory to test if a given time series contains oscillatory components.
Keywords
60K35, complex Gaussian random vector, CR calculation, kernel regression, Synchrosqueezing transform, time series analysis
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